The Grassmannian

The Grassmannian is a mathematical space that represents all possible ways to select a flat, straight surface (called a subspace) within a higher-dimensional space. For example, in three dimensions, it describes all possible planes passing through the origin. It helps mathematicians and scientists understand how these subspaces relate and vary, forming a structured way to study their geometry. Think of it as a catalog of all possible flat directions or surfaces of a certain size within a larger space, which is useful in fields like geometry, physics, and data analysis.